Controlled scan pattern transition in coherent lidar

ABSTRACT

A coherent lidar system, a method of operating the coherent lidar system and a vehicle including the coherent lidar system involve a beam steering device to direct output light from the system within a field of view. A first series of positions of the beam steering device defines a first scan pattern within the field of view and a second series of positions of the beam steering device defines a second scan pattern within the field of view. The coherent lidar system includes a controller to provide transition positions to the beam steering device to transition the beam steering device from the first scan pattern to the second scan pattern. The transition positions follow a basis spline (B-spline) function.

INTRODUCTION

The subject disclosure relates to controlled scan pattern transition ina coherent lidar system.

Vehicles (e.g., automobiles, trucks, construction equipment, farmequipment, automated factory equipment) increasingly include sensorsthat obtain information about the vehicle operation and the environmentaround the vehicle. Some sensors, such as cameras, radio detection andranging (radar) systems, and light detection and ranging (lidar) systemscan detect and track objects in the vicinity of the vehicle. A coherentlidar system transmits frequency modulated continuous wave (FMCW) lightand processes reflected beams to determine information about the target.By determining the relative location and heading of objects around thevehicle, vehicle operation may be augmented or automated to improvesafety and performance. For example, sensor information may be used toissue alerts to the driver of the vehicle or to operate vehicle systems(e.g., collision avoidance systems, adaptive cruise control system,autonomous driving system). Sensors like the radar system and the lidarsystem may perform a scan over a given field of view. In the case of thelidar system, a beam steering device may be used to direct the lightbeam, one transmission at a time, in a pattern that represents a coarsescan over the field of view. If a target is detected during that coarsescan, the lidar system may then reduce the area over which a finer scanis performed. Accordingly, it is desirable to provide controlled scanpattern transition in a coherent lidar system

SUMMARY

In one exemplary embodiment, a coherent lidar system includes a beamsteering device to direct output light from the system within a field ofview. A first series of positions of the beam steering device defines afirst scan pattern within the field of view and a second series ofpositions of the beam steering device defines a second scan patternwithin the field of view. The system also includes a controller toprovide transition positions to the beam steering device to transitionthe beam steering device from the first scan pattern to the second scanpattern. The transition positions follow a basis spline (B-spline)function.

In addition to one or more of the features described herein, thecontroller determines the transition positions based on determining anumber of segments N of the B-spline.

In addition to one or more of the features described herein, thecontroller determines the number of segments N by minimizing a value ofN without a velocity of the beam steering device exceeding a maximumvalue based on the velocity increasing as the value of N decreases.

In addition to one or more of the features described herein, thecontroller calculates the B-spline function based on determining anumber of knots. The number of knots indicates a number of changes ofdirection required to reach an initial position of the second scanpattern from a final position of the first scan pattern, the first scanpattern ending with a position vector

and velocity vector

and the second scan pattern starting with a position vector

′ and velocity vector

′.

In addition to one or more of the features described herein, thecontroller determines whether the number of knots is one or two based onwhether the velocity vector

and the velocity vector

′ are parallel and based on scalar parameters u and u′ that are solvedbased on the position vector

, the velocity vector

, the position vector

′, and the velocity vector

′.

In addition to one or more of the features described herein, thecontroller determines that the number of knots is one based on thevelocity vector

and the velocity vector

′ being parallel and a dot product of the velocity vector

and the velocity vector

′ being negative or based on the velocity vector

and the velocity vector

′ not being parallel and sign functions of u and u′ being unequal.

In addition to one or more of the features described herein, thecontroller determines that the number of knots is two based on thevelocity vector

and the velocity vector

′ being parallel and a dot product of the velocity vector

and the velocity vector

′ being non-negative or based on the velocity vector

and the velocity vector

′ not being parallel and sign functions of u and u′ being equal.

In addition to one or more of the features described herein, thecontroller determines the second scan pattern based on a detection of atarget in the first scan pattern.

In addition to one or more of the features described herein, the systemis a monostatic system or a bistatic system.

In addition to one or more of the features described herein, the systemis included on or within a vehicle and detects a location and speed ofan object relative to the vehicle.

In another exemplary embodiment, a method of operating a coherent lidarsystem includes adjusting a beam steering device to direct output lightfrom the system within a field of view. The adjusting the beam steeringdevice to a first series of positions defines a first scan patternwithin the field of view and adjusting the beam steering device to asecond series of positions defines a second scan pattern within thefield of view. The method also includes providing transition positionsto the beam steering device to transition the beam steering device fromthe first scan pattern to the second scan pattern. The transitionpositions follow a basis spline (B-spline) function.

In addition to one or more of the features described herein, the methodalso includes determining the transition positions based on determininga number of segments N of the B-spline.

In addition to one or more of the features described herein, thedetermining the number of segments is based on minimizing a value of Nwithout a velocity of the beam steering device exceeding a maximum valuebased on the velocity increasing as the value of N decreases.

In addition to one or more of the features described herein, the methodalso includes calculating the B-spline function based on determining anumber of knots, the number of knots indicating a number of changes ofdirection required to reach an initial position of the second scanpattern from a final position of the first scan pattern, the first scanpattern ending with a position vector

and velocity vector

and the second scan pattern starting with a position vector

′ and velocity vector

′.

In addition to one or more of the features described herein, the methodalso includes determining whether the number of knots is one or twobased on determining whether the velocity vector

and the velocity vector

′ are parallel and based on determining scalar parameters u and u′ thatare solved based on the position vector

, the velocity vector

, the position vector

, and the velocity vector

′.

In yet another exemplary embodiment, a vehicle includes a coherent lidarsystem that includes a beam steering device to direct output light fromthe system within a field of view. The first series of positions of thebeam steering device defines a first scan pattern within the field ofview and a second series of positions of the beam steering devicedefines a second scan pattern within the field of view. The coherentlidar system also includes a controller to provide transition positionsto the beam steering device to transition the beam steering device fromthe first scan pattern to the second scan pattern. The transitionpositions follow a basis spline (B-spline) function. The vehicle alsoincludes a vehicle controller to augment or automate operation of thevehicle based on information obtained from the coherent lidar system.

In addition to one or more of the features described herein, thecontroller determines the transition positions based on determining anumber of segments N of the B-spline.

In addition to one or more of the features described herein, thecontroller determines the number of segments N by minimizing a value ofN without a velocity of the beam steering device exceeding a maximumvalue based on the velocity increasing as the value of N decreases.

In addition to one or more of the features described herein, thecontroller calculates the B-spline function based on determining anumber of knots, the number of knots indicating a number of changes ofdirection required to reach an initial position of the second scanpattern from a final position of the first scan pattern, the first scanpattern ending with a position vector

and velocity vector

and the second scan pattern starting with a position vector

′ and velocity vector

′.

In addition to one or more of the features described herein, thecontroller determines whether the number of knots is one or two based onwhether the velocity vector

and the velocity vector

′ are parallel and based on scalar parameters u and u′ that are solvedbased on the position vector

, the velocity vector

, the position vector

′, and the velocity vector

′.

The above features and advantages, and other features and advantages ofthe disclosure are readily apparent from the following detaileddescription when taken in connection with the accompanying drawings.

BRIEF DESCRIPTION OF THE DRAWINGS

Other features, advantages and details appear, by way of example only,in the following detailed description, the detailed descriptionreferring to the drawings in which:

FIG. 1 is a block diagram of a scenario involving a coherent lidarsystem according to one or more embodiments;

FIG. 2 is a block diagram of a coherent lidar system with a controlledscan pattern transition according to one or more embodiments;

FIG. 3 is a block diagram of a coherent lidar system with controlledscan pattern transition according to alternate one or more embodiments;

FIG. 4 shows an exemplary coarse scan and an exemplary fine scanfacilitated by controlled scan pattern transition according to alternateone or more embodiments;

FIGS. 5A-5F illustrates different scenarios for the initial positionvector

and final position vector

′ to describe additional processes in the determination of thetransition according to embodiments;

FIG. 6 shows an exemplary transition determined according to one or moreembodiments; and

FIG. 7 is a process flow of a method of performing a controlled scanpattern transition with the beam steering device of a coherent lidarsystem according to one or more embodiments.

DETAILED DESCRIPTION

The following description is merely exemplary in nature and is notintended to limit the present disclosure, its application or uses. Itshould be understood that throughout the drawings, correspondingreference numerals indicate like or corresponding parts and features.

As previously noted, sensors may be used to augment vehicle operation orto operate an autonomous vehicle. As also noted, one type of sensor is acoherent lidar system that transmits an FMCW signal. The system takesadvantage of phase coherence between the transmitted FMCW signal and areflected signal resulting from reflection of the transmitted FMCWsignal by a target. The interference between the reflected signal and acopy of the transmitted signal is used to determine information such astarget distance and speed. The coherent lidar system differs from priortime-of-flight lidar systems that transmit a series of pulses and usethe duration for transmission of each pulse and reception of theresulting reflection to determine a set of distances for the target. Thecoherent lidar system may perform a coarse scan over a field of view andthen perform a finer scan over a more limited area based on identifyinga target during the coarse scan, for example.

A beam steering device facilitates the scan by focusing light in aspecified area. In many scenarios, it may be advantageous to reduce thefield of view of a sensor from a wide one, covered by a coarse scan, toa smaller one, covered by a fine scan, in order to increase the sensor'sresolution. The transition of the beam steering device from the end of acoarse scan to a starting point of the area for a fine scan can resultin ringing or oscillations of the mirror if the transition is done tooquickly. However, too slow a transition may result in the target movingout of the area determined for the finer scan before the scan isstarted. Embodiments of the systems and methods detailed herein relateto controlled scan pattern transition in a coherent lidar system.Specifically, a trajectory is determined to transition the beam steeringdevice from the coarse scan to the fine scan.

In accordance with an exemplary embodiment, FIG. 1 is a block diagram ofa scenario involving a coherent lidar system 110 with a controlled scanpattern transition 430 (FIG. 4). The vehicle 100 shown in FIG. 1 is anautomobile 101. A coherent lidar system 110, further detailed withreference to FIG. 2, is shown on the roof of the automobile 101.According to alternate or additional embodiments, one or more lidarsystems 110 may be located elsewhere on the vehicle 100. Another sensor115 (e.g., camera, microphone, radar system) is shown, as well.Information obtained by the lidar system 110 and one or more othersensors 115 may be provided to a controller 120 (e.g., electroniccontrol unit (ECU)).

The controller 120 may use the information to control one or morevehicle systems 130. In an exemplary embodiment, the vehicle 100 may bean autonomous vehicle and the controller 120 may perform known vehicleoperational control using information from the lidar system 110 andother sources. In alternate embodiments, the controller 120 may augmentvehicle operation using information from the lidar system 110 and othersources as part of a known system (e.g., collision avoidance system,adaptive cruise control system). The lidar system 110 and one or moreother sensors 115 may be used to detect objects 140, such as thepedestrian 145 shown in FIG. 1. The controller 120 may includeprocessing circuitry that may include an application specific integratedcircuit (ASIC), an electronic circuit, a processor (shared, dedicated,or group) and memory that executes one or more software or firmwareprograms, a combinational logic circuit, and/or other suitablecomponents that provide the described functionality.

FIG. 2 is a block diagram of a coherent lidar system 110 with acontrolled scan pattern transition 430 according to one or moreembodiments. The exemplary lidar system 110 shown in FIG. 2 is amonostatic system that uses the same path for light output from thelidar system 110 as an output signal 236 and light obtained by the lidarsystem 110 as a receive beam 238. The lidar system 110 includes a lightsource 210. The light source 210 may be a laser diode such as adistributed feedback (DFB) laser according to an exemplary embodiment.The light source 210 outputs a continuous wave of light, which exhibitsa constant amplitude. The next stage in the light output system includesan optical resonator 220.

The resonator 220 is an external optical cavity, external to the lightsource 210 and, according to the exemplary embodiment shown in FIG. 2, acontrolled voltage 225 using a voltage source is applied to theresonator 220 to perform electro-optical modulation and modulate thefrequency of the continuous wave of light in the resonator 220 toproduce FMCW light 227. According to the exemplary embodiment, thefeedback of some light from the resonator 220 to the light source 210means that the light generated within the light source 210 and the lightoutput by the resonator 220 are modulated synchronously. The controlledvoltage 225 may be increased or decreased linearly in order to producelight that exhibits linear frequency modulation (i.e., a linear FMCWsignal). Alternately, the controlled voltage 225 may be variednon-linearly to produce light that exhibits non-linear frequencymodulation.

According to alternate embodiments, the FMCW light 227 may be obtainedby modulating the frequency at the light source 210 itself. In thiscase, the controlled voltage 225 applied to the resonator 220, as shownin FIG. 2, may be applied directly to block 210. For example, the biascurrent of the laser chip may be changed or a physical cavity or mirrorof the light source 210 may be modulated. This modulation may beimplemented by piezoelectric or microelectromechanical systems (MEMS)actuation, for example. As FIG. 2 indicates, an optional opticalamplifier 230 may be used to amplify the FMCW light 227 output by theresonator 220 to produce the FMCW signal 235.

A beam splitter 240 is used to split the FMCW signal 235 into an outputsignal 236 and a local oscillator (LO) signal 237. Both the outputsignal 236 and the LO signal 237 exhibit the frequency modulationimparted by the controlled voltage 225, or other modulator. The beamsplitter 240 may be an on-chip waveguide splitter, for example. Theoutput signal 236 is provided to a light circulating element, acirculator 250, which is necessary in the monostatic system shown inFIG. 2. The circulator 250 directs the output signal 236 out of thelidar system 110 through an aperture lens 255 (e.g., a monocentric lenslike a ball lens).

A beam steering device 257 ensures proper alignment of the output signal236 exiting the lidar system 110 and proper alignment of the receivebeam 238 that enters the lidar system 110 and must be properly alignedfor ultimate interference at the photodiodes 280. The beam steeringdevice 257 may be a reflector. According to the exemplary embodimentshown in FIG. 2, the beam steering device 257 is a two-dimensional MEMSscanning mirror. In alternate embodiments, the beam steering device 257,which performs two-dimensional beam steering, may be a mirrorgalvanometer, Risley prism pairs, an optical phased array, or liquidcrystal beam steering device. Control of this beam steering device 257,as further discussed with reference to FIGS. 4 and 5, facilitates thecontrolled scan pattern transition 430 according to one or moreembodiments.

A beam steering controller 200 is shown in FIG. 2 and provides a beamsteering control signal 201 to the beam steering device 257. Inalternate embodiments, the controller 120 may perform this function andsend the beam steering control signal 201 from outside the lidar system110. Like the controller 120, the beam steering controller 200 mayinclude processing circuitry that may include an application specificintegrated circuit (ASIC), an electronic circuit, a processor (shared,dedicated, or group) and memory that executes one or more software orfirmware programs, a combinational logic circuit, and/or other suitablecomponents that provide the described functionality.

A light conveyer 256 (e.g., fiber taper bundle, micro lens array andstatic mirror) conveys light between the beam steering device 257 andthe aperture lens 255. If a target 140 is in the field of view of thelidar system 110, as in the example shown in FIG. 2, the FMCW outputsignal 236 output from the lidar system 110 is scattered by the target140. Some of that scattered light reenters the lidar system 110 as areceive beam 238. The receive beam 238 enters the aperture lens 255, isconveyed by the light conveyer 256 to the beam steering device 257, andis directed by the circulator 250 to a reflector 258. The reflector 258directs the receive beam 238 to an optional optical amplifier 260,according to one or more embodiments.

While the optical amplifier 260 is shown between the reflector 258 andan alignment element 270 in FIG. 2, the optical amplifier 260 mayinstead be located between the circulator 250 and the reflector 258,along the path indicated as “A.” According to exemplary embodiments, theoptical amplifier 260 may include coupling lenses to direct the receivebeam 238 into the optical amplifier 260 without loss. The opticalamplifier 260 may also include shaping optics to ensure that theamplified receive beam 265 provided by the optical amplifier 260 has thecorrect profile.

The amplified receive beam 265 is provided to the alignment element 270in which with the amplified receive beam 265 is aligned with the LOsignal 237. The alignment element 270 ensures that the amplified receivebeam 265 and the LO signal 237 are co-linear and splits the output intotwo co-linear signals 272 a, 272 b (generally referred to as 272). Theco-linear signals 272 a, 272 b are respectively directed tophotodetectors 280 a, 280 b (generally referred to as 280). As FIG. 2indicates, one of the co-linear signal 272 a is reflected by a reflector275 in order to be directed into the corresponding photodetector 280 a.The amplified receive beam 265 and LO signal 237, which are aligned inthe co-linear signal 272, interfere with each other in thephotodetectors 280. The interference between the amplified receive beam265 and the LO signal 237 results in a coherent combination of the twobeams. Thus, the lidar system 110 is referred to as a coherent lidarsystem, unlike the time-of-flight systems. The interference in eachphotodetector 280 is effectively like performing an autocorrelationfunction to identify an amplified receive beam 265 that resulted fromthe output signal 236. This prevents errant light from another lightsource outside the lidar system 110, which is within the field of viewof the lidar system 110, from being mistaken for a receive beam 238 thatis reflected by a target 140.

The photodetectors 280 are semiconductor devices that convert the resultof the interference between the amplified receive beam 265 and the LOsignal 237 in each co-linear signal 272 into electrical currents 285 a,285 b (generally referred to as 285). Two photodetectors 280 are used inaccordance with a known balanced detector technique to cancel noise thatis common to both photodetectors 280. The electrical currents 285 fromeach of the photodetectors 280 are combined and processed to obtaininformation such as range to the target 140, speed of the target 140,and other information according to known processing techniques. Theprocessing may be performed within the lidar system 110 by a processor290 or outside the lidar system 110 by the controller 120, for example.The processor 290 may include processing circuitry similar to thatdiscussed for the controller 120.

FIG. 3 is a block diagram of a coherent lidar system 110 with controlledscan pattern transition 430 according to alternate one or moreembodiments. A bistatic lidar system 110 is shown in the exemplaryembodiment of FIG. 3. Most of the bistatic lidar system 110, shown inFIG. 3, is identical to the monostatic lidar system 110, shown in FIG.2. Thus, the components detailed with reference to FIG. 2 are notdiscussed again. As previously noted, the primary difference between themonostatic and bistatic systems is in the inclusion, in the bistaticsystem, of separate aperture lenses 255 a, 255 b (generally referred toas 255), light conveyers 256 a, 256 b (generally referred to as 256),and beam steering devices 257 a, 257 b (generally referred to as 257)for the output signal 236 and receive beam 238. As such a circulator 250is not needed in the bistatic system of FIG. 3.

FIG. 4 shows an exemplary coarse scan 410 and an exemplary fine scan 420facilitated by controlled scan pattern transition 430 according toalternate one or more embodiments. The transition 430 and the fine scan420 may be determined by the beam steering controller 200 or anothercontroller 120 in the vehicle 100. The transition 430 may be initiatedbased on the detection of a target 140 during the coarse scan 410, forexample, such that the fine scan 420 covers a narrow field of viewdefined by the position of the detected target 140. Although the exampleshown in FIG. 4 is from a coarse scan 410 to a fine scan 420, thetransition 430 is not limited to be between any particular scan type orbetween relatively broader or narrower scans. For example, thetransition 430 may be between two coarse scans 410 that each cover adifferent part of the overall field of view.

The transition 430 is implemented as a basis spline (B-spline) accordingto an exemplary embodiment. The B-spline that defines the transition 430is a vector function

(t) that satisfies the following boundary condition:

(0)=

  [EQ. 1]

According to EQ. 1, at time t=0, the beginning of the transition 430,the initial position of the beam steering device 257 is

. The position vector

, provides a position direction relative to an origin. Generally theorigin is the center of the overall field of view of the lidar system110, which may correspond with the default position of the beam steeringdevice 257. Another boundary condition that the vector function

(t) must satisfy is:

(T)=

′  [EQ. 2]

At time t=T, at the end of the transition 430, the final position of thebeam steering device 257, which is the initial position to begin thefine scan 420, is given by

′. A third boundary condition is given by:

$\begin{matrix}{{\frac{d\overset{\rightharpoonup}{f}}{dt}_{t = 0}} = {\frac{d\overset{\rightharpoonup}{r}}{dt} = \overset{\rightharpoonup}{v}}} & \left\lbrack {{EQ}.\mspace{14mu} 3} \right\rbrack\end{matrix}$

In EQ. 3,

is the instantaneous velocity at which the beam steering device 257 ismoving at the end of the coarse scan 410. The final boundary conditionis given by:

$\begin{matrix}{{\frac{d\overset{\rightharpoonup}{f}}{dt}_{t = T}} = {\frac{d{\overset{\rightharpoonup}{r}}^{\prime}}{dt} = {\overset{\rightharpoonup}{v}}^{\prime}}} & \left\lbrack {{EQ}.\mspace{14mu} 4} \right\rbrack\end{matrix}$

In EQ. 4,

′ is the instantaneous velocity at which the beam steering device 257 ismoving at the beginning of the fine scan 420.

Additional conditions that are used to solve for the B-spline definingthe transition 430 include the following:

$\begin{matrix}{{\overset{\rightharpoonup}{f}} < {{\overset{\rightharpoonup}{r}}_{\max}\mspace{14mu} {for}\mspace{14mu} {all}\mspace{14mu} 0} < t < T} & \left\lbrack {{EQ}.\mspace{14mu} 5} \right\rbrack \\{\frac{d\overset{\rightharpoonup}{f}}{dt} < {{\overset{\rightharpoonup}{v}}_{\max}\mspace{14mu} {for}\mspace{14mu} {all}\mspace{14mu} 0} < t < T} & \left\lbrack {{EQ}.\mspace{14mu} 6} \right\rbrack\end{matrix}$

According to EQ. 5, the vector function

(t) cannot have a position direction relative to the origin thatrequires the beam steering device 257 to exceed its maximum steeringposition during the transition 430. For example, when the beam steeringdevice 257 is a MEMS scanning mirror, the transition 430 cannot requirethe maximum tilt angle of the mirror to be exceeded. According to EQ. 6,a maximum velocity cannot be exceeded during the transition 430.

FIGS. 5A-5F illustrates different scenarios for the initial positionvector

, final position vector

′, initial velocity vector

, and final velocity vector

′ to describe additional processes in the determination of thetransition 430 according to embodiments. Specifically, the scenariosillustrate the determination of whether one or two knots 510 arerequired. Knots 510 are breakpoints or places where the piecewisepolynomial functions that make up the B-spline function meet. FIG. 5Aindicates that the initial velocity vector

and final velocity vector

′ are parallel relative to the origin but directed in oppositedirections. Generally, a comparison of FIGS. 5A and 5B indicates thatthe parallel velocity vectors

and

′ moving in the same direction, as in FIG. 5B, result in two changes ofdirection or two knots 510 being needed, while the parallel velocityvectors

and

′ moving in opposite directions, as in FIG. 5A, results in one change ofdirection or one knot 510 being needed. A comparison of FIGS. 5C, 5D,5E, and 5F indicates that the perpendicular velocity vectors

and

′ moving away from each other, as in FIGS. 5C and 5E, result in onechange of direction or one knot 510 being needed, while theperpendicular velocity vectors

and

′ moving toward from each other, as in FIGS. 5D and 5F, result in twochanges of direction or two knots 510 being needed. These observationsare used in the determination of the number of knots 510, as discussedwith reference to FIG. 7.

FIG. 6 shows an exemplary transition 430 determined according to one ormore embodiments. The exemplary transition 430 shown in FIG. 6 includestwo knots 510. Given the boundary conditions and other conditionsdiscussed with reference to EQS. 1 through 6, and also based ondetermining whether one or two knots 510 are needed for the transition430, the number of equal-time segments 610 is determined for thetransition 430. Specifically, the end points of each segment 610indicate positions corresponding with the beam steering device 257, andequal-time segments 610 refers to the fact that each segment 610 may notrepresent the same distance but does represent the same duration for thebeam steering device 257 to change positions. In alternate embodiments,the segments 610 may not be equal-time segments.

In FIG. 6, 10 segments 610 (N=10) are shown for the B-spline thatdefines the transition 430. The determination of the number N ofsegments 610 is based on the fact that the velocity of the beam steeringdevice 257, in transitioning from segment 610 to segment 610, decreasesas the number N of the segments 610 increases. Stated another way, theduration T of the transition 430 increases as the number N of thesegments 610 increases. Because the goal is to minimize the duration Tof the transition 430, the number N of the segments 610 should beminimized. At the same time, the number N of the segments 610 cannot beselected to be so low that the instantaneous velocity at any point alongthe B-spline, which increases as N decreases, exceeds the maximumvelocity,

_(max).

FIG. 7 is a process flow 700 of a method of performing a controlled scanpattern transition 430 with the beam steering device 257 according toone or more embodiments. The processes discussed with reference to FIG.7 may be performed by the beam steering controller 200 or anothercontroller 120 in the vehicle 100 according to exemplary embodiments. Atblock 710, receiving a new scan pattern includes receiving the patternof the fine scan 420, according to the exemplary case shown in FIG. 4.Determining the last position and velocity of the current scan and thestart position and velocity of the new scan, at block 720, refers toobtaining

,

′, and

′, respectively.

At block 730, a check is done of whether the velocity vectors

and

′ are parallel. This is the case for the scenarios shown in FIGS. 5A and5B. If the velocity vectors are parallel, the process at block 740 isperformed. At block 740, a check is done of whether a dot product of thevelocity vectors

and

′ is negative. If the dot product of the velocity vectors

and

′ is negative according to the check at block 740, then calculating theB-spline with one knot 510, at block 750, is performed, as is the caseof FIG. 5A. If the dot product of the velocity vectors

and

′ is not negative, according to the check at block 740, then calculatingthe B-spline with two knots 510, at block 770, is performed, as is thecase of FIG. 5B.

If the velocity vectors

and

′ are not parallel, according to the check at block 730, then theprocess at block 760 is performed. At block 760, the following vectorequation is solved to determine scalar parameters u and u′, whichrepresent, respectively, relative time coordinates for the trajectorywith v originating at r and the trajectory with v′ originating at r′:

+

u=

+

u′  [EQ. 7]

The position and velocity vectors are two-dimensional vectors. Thus, theposition vector,

may be defined as

=

r₁, r₂

, for the position vector

′ may be defined as

′=

r₁′, r₂′

, velocity vector

may be defined as

=

v₁, v₂

, and velocity vector

′ may be defined as

′=

v₁′, v₂′

. In the exemplary embodiment, this coordinate decomposition isperformed in a spherical angle space, with the r₁ coordinaterepresenting angle in azimuth (ϕ) and the r₂ coordinate representingangle in elevation (θ). In alternate embodiments, the coordinatedecomposition may be performed for any two-dimensional basis, such asCartesian or polar coordinates, with r₁ representing the coordinatealong the first basis vector and r₂ the coordinate along the secondbasis vector. Thus, EQ. 7 represents a system of two linear equationswhich may be solved simultaneously for u and u′, with the closed-formsolution:

$\begin{matrix}{{u = \frac{{v_{1}^{\prime}\left( {r_{2}^{\prime} - r_{2}} \right)} + {v_{2}^{\prime}\left( {r_{1} - r_{1}^{\prime}} \right)}}{{v_{2}v_{1}^{\prime}} - {v_{1}v_{2}^{\prime}}}},} & \left\lbrack {{EQ}.\mspace{14mu} 8} \right\rbrack \\{u^{\prime} = \frac{{v_{1}\left( {r_{2}^{\prime} - r_{2}} \right)} + {v_{2}\left( {r_{1} - r_{1}^{\prime}} \right)}}{{v_{2}v_{1}^{\prime}} - {v_{1}v_{2}^{\prime}}}} & \left\lbrack {{EQ}.\mspace{14mu} 9} \right\rbrack\end{matrix}$

The check, at block 730, of whether the velocity vectors

and

′ are parallel accounts for the case in which EQ. 7 is degenerate (i.e.there is no solution for u and u′, which occurs when v₂v₁′=v₁v₂′).

A check is then done, at block 765, of whether the sign function of uand u′ are equal. If they are equal, according to the check at block765, then calculating the B-spline with two knots 510, at block 770, isperformed, as is the case of FIGS. 5D and 5F. If the sign functions of uand u′ are not equal, according to the check at block 765, thencalculating the B-spline with one knot 510, at block 750, is performed,as is the case of FIGS. 5C and 5E.

At block 780, determining the number N of segments 610 is performedbased on the trade-off between the number of segments N and the velocityof the beam steering device 257 during the transition 430, as discussedwith reference to FIG. 6. Once the number N of segments 610 isdetermined, the process at block 780 also includes segmenting theB-spline that was calculated either at block 750 or at block 770. Atblock 790, determining the beam steering device 257 positions in orderto traverse the B-spline segments 610 results in the beam steeringcontroller 200 or another controller 120 moving the beam steering device257 through the transition 430 to the new scan pattern.

While the above disclosure has been described with reference toexemplary embodiments, it will be understood by those skilled in the artthat various changes may be made and equivalents may be substituted forelements thereof without departing from its scope. In addition, manymodifications may be made to adapt a particular situation or material tothe teachings of the disclosure without departing from the essentialscope thereof. Therefore, it is intended that the present disclosure notbe limited to the particular embodiments disclosed, but will include allembodiments falling within the scope thereof

What is claimed is:
 1. A coherent lidar system, comprising: a beamsteering device configured to direct output light from the system withina field of view, wherein a first series of positions of the beamsteering device defines a first scan pattern within the field of viewand a second series of positions of the beam steering device defines asecond scan pattern within the field of view; and a controllerconfigured to provide transition positions to the beam steering deviceto transition the beam steering device from the first scan pattern tothe second scan pattern, wherein the transition positions follow a basisspline (B-spline) function.
 2. The system according to claim 1, whereinthe controller is further configured to determine the transitionpositions based on determining a number of segments N of the B-spline.3. The system according to claim 2, wherein the controller is furtherconfigured to determine the number of segments N by minimizing a valueof N without a velocity of the beam steering device exceeding a maximumvalue based on the velocity increasing as the value of N decreases. 4.The system according to claim 1, wherein the controller is furtherconfigured to calculate the B-spline function based on determining anumber of knots, the number of knots indicating a number of changes ofdirection required to reach an initial position of the second scanpattern from a final position of the first scan pattern, the first scanpattern ending with a position vector

and velocity vector

and the second scan pattern starting with a position vector

′ and velocity vector

′.
 5. The system according to claim 4, wherein the controller is furtherconfigured to determine whether the number of knots is one or two basedon whether the velocity vector

and the velocity vector

′ are parallel and based on scalar parameters u and u′ that are solvedbased on the position vector

, the velocity vector

, the position vector

′, and the velocity vector

′.
 6. The system according to claim 5, wherein the controller is furtherconfigured to determine that the number of knots is one based on thevelocity vector

and the velocity vector

′ being parallel and a dot product of the velocity vector

and the velocity vector

′ being negative or based on the velocity vector

and the velocity vector

′ not being parallel and sign functions of u and u′ being unequal. 7.The system according to claim 5, wherein the controller is furtherconfigured to determine that the number of knots is two based on thevelocity vector

and the velocity vector

′ being parallel and a dot product of the velocity vector

and the velocity vector

′ being non-negative or based on the velocity vector

and the velocity vector

′ not being parallel and sign functions of u and u′ being equal.
 8. Thesystem according to claim 1, wherein the controller is furtherconfigured to determine the second scan pattern based on a detection ofa target in the first scan pattern.
 9. The system according to claim 1,wherein the system is a monostatic system or a bistatic system.
 10. Thesystem according to claim 1, wherein the system is included on or withina vehicle and is configured to detect a location and speed of an objectrelative to the vehicle.
 11. A method of operating a coherent lidarsystem, the method comprising: adjusting a beam steering device todirect output light from the system within a field of view, wherein theadjusting the beam steering device to a first series of positionsdefines a first scan pattern within the field of view and adjusting thebeam steering device to a second series of positions defines a secondscan pattern within the field of view; and providing transitionpositions to the beam steering device to transition the beam steeringdevice from the first scan pattern to the second scan pattern, whereinthe transition positions follow a basis spline (B-spline) function. 12.The method according to claim 11, further comprising determining thetransition positions based on determining a number of segments N of theB-spline.
 13. The method according to claim 12, wherein the determiningthe number of segments is based on minimizing a value of N without avelocity of the beam steering device exceeding a maximum value based onthe velocity increasing as the value of N decreases.
 14. The methodaccording to claim 11, further comprising calculating the B-splinefunction based on determining a number of knots, the number of knotsindicating a number of changes of direction required to reach an initialposition of the second scan pattern from a final position of the firstscan pattern, the first scan pattern ending with a position vector

and velocity vector

and the second scan pattern starting with a position vector

′ and velocity vector

′.
 15. The method according to claim 14, further comprising determiningwhether the number of knots is one or two based on determining whetherthe velocity vector

and the velocity vector

′ are parallel and based on determining scalar parameters u and u′ thatare solved based on the position vector

, the velocity vector

, the position vector

′, and the velocity vector

′.
 16. A vehicle, comprising: a coherent lidar system comprising: a beamsteering device configured to direct output light from the system withina field of view, wherein a first series of positions of the beamsteering device defines a first scan pattern within the field of viewand a second series of positions of the beam steering device defines asecond scan pattern within the field of view; and a controllerconfigured to provide transition positions to the beam steering deviceto transition the beam steering device from the first scan pattern tothe second scan pattern, wherein the transition positions follow a basisspline (B-spline) function; and a vehicle controller configured toaugment or automate operation of the vehicle based on informationobtained from the coherent lidar system.
 17. The vehicle according toclaim 16, wherein the controller is further configured to determine thetransition positions based on determining a number of segments N of theB-spline.
 18. The vehicle according to claim 17, wherein the controlleris further configured to determine the number of segments N byminimizing a value of N without a velocity of the beam steering deviceexceeding a maximum value based on the velocity increasing as the valueof N decreases.
 19. The vehicle according to claim 16, wherein thecontroller is further configured to calculate the B-spline functionbased on determining a number of knots, the number of knots indicating anumber of changes of direction required to reach an initial position ofthe second scan pattern from a final position of the first scan pattern,the first scan pattern ending with a position vector

and velocity vector

and the second scan pattern starting with a position vector

′ and velocity vector

′.
 20. The vehicle according to claim 19, wherein the controller isfurther configured to determine whether the number of knots is one ortwo based on whether the velocity vector

and the velocity vector

′ are parallel and based on scalar parameters u and u′ that are solvedbased on the position vector

, the velocity vector

, the position vector

′, and the velocity vector

′.